Distributed scalar quantization for computing: High-resolution analysis and extensions

IEEE Transactions on Information Theory

Volumn 57, Issue 8, 2011, Pages 5298-5325

  Misra, Vinith ^a   Goyal, Vivek K ^b   Varshney, Lav R ^c  

^a Stanford University   (United States)

^b Department of Electrical Engineering and Computer Science   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Asymptotic quantization theory; distributed source coding; optimal point density function; rate distortion theory

Indexed keywords

ASYMPTOTIC OPTIMALITY; ASYMPTOTIC QUANTIZATION; CENTRALIZED COMPUTATION; COMPANDING; DISTRIBUTED SOURCE CODING; HIGH RESOLUTION ANALYSIS; LARGE CLASS; MEAN SQUARED ERROR; OPTIMAL POINTS; QUANTIZERS; RATE-DISTORTION THEORY; SCALAR QUANTIZATION; SCALAR QUANTIZERS; SINGLE-BIT; SMOOTHNESS CONDITIONS;

ENTROPY;

EID: 79955746919     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2158882     Document Type: Review

References (36)

1. V. Doshi, D. Shah, and M. Mědard, "Source coding with distortion through graph coloring," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2007), Jun. 2007, pp. 1501-1505.
2. D. Slepian and J. K.Wolf, "Noiseless coding of correlated information sources," IEEE Trans. Inf. Theory, vol. IT-19, no. 4, pp. 471-480, Jul. 1973.
3. S. D. Servetto, "Achievable rates for multiterminal source coding with scalar quantizers," in Proc. Conf. Rec. 39th Asilomar Conf. Signals, Syst. Comput., Oct. 2005, pp. 1762-1766. (Pubitemid 46350609)
4. A. B. Wagner, S. Tavildar, and P. Viswanath, "Rate region of the quadratic Gaussian two-terminal source-coding problem," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 1938-1961, May 2008. (Pubitemid 351689542)
5. R. Zamir and T. Berger, "Multiterminal source coding with high resolution," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 106-117, Jan. 1999.
6. A. D.Wyner and J. Ziv, "The rate-distortion function for source coding with side information at the decoder," IEEE Trans. Inf. Theory, vol. IT-22, no. 1, pp. 1-10, Jan. 1976.
7. R. Zamir, "The rate loss in the Wyner-Ziv problem," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 2073-2084, Nov. 1996. (Pubitemid 126771536)
8. D. Rebollo-Monedero, S. Rane, A. Aaron, and B. Girod, "High-rate quantization and transform coding with side information at the decoder," Signal Process., vol. 86, no. 11, pp. 3160-3179, Nov. 2006. (Pubitemid 44331437)
9. Z. Liu, S. Cheng, A. D. Liveris, and Z. Xiong, "Slepian-Wolf coded nested lattice quantization for Wyner-Ziv coding: High-rate performance analysis and code design," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4358-4379, Oct. 2006. (Pubitemid 46453625)
10. E. Martinian, G. Wornell, and R. Zamir, "Source coding with encoder side information," IEEE Trans. Inf. Theory, vol. 54, no. 10, pp. 4638-4665, Oct. 2008.
11. T. Linder, R. Zamir, and K. Zeger, "On source coding with side-information- dependent distortion measures," IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2697-2704, Nov. 2000. (Pubitemid 32090053)
12. H. Yamamoto, "Wyner-Ziv theory for a general function of the correlated sources," IEEE Trans. Inf. Theory, vol. IT-28, no. 5, pp. 803-807, Sep. 1982.
13. H. Feng, M. Effros, and S. A. Savari, "Functional source coding for networks with receiver side information," in Proc. 42nd Annu. Allerton Conf. Commun. Control Comput., Sep. 2004, pp. 1419-1427.
14. A. Orlitsky and J. R. Roche, "Coding for computing," IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 903-917, Mar. 2001. (Pubitemid 32425425)
15. T. S. Han and K. Kobayashi, "A dichotomy of functions F(X,Y) of correlated sources (X,Y) from the viewpoint of the achievable rate region," IEEE Trans. Inf. Theory, vol. IT-33, no. 1, pp. 69-76, Jan. 1987.
16. V. Doshi, D. Shah, M. Mědard, and S. Jaggi, "Distributed functional compression through graph coloring," in Proc. IEEE Data Compress. Conf. (DCC 2007), Mar. 2007, pp. 93-102. (Pubitemid 47201861)
17. H. Yamamoto and K. Itoh, "Source coding theory for multiterminal communication systems with a remote source," Trans. IECE Japan, vol. E63, no. 10, pp. 700-706, Oct. 1980. (Pubitemid 11459988)
18. J. Körner and K. Marton, "How to encode the modulo-two sum of binary sources," IEEE Trans. Inf. Theory, vol. IT-25, no. 2, pp. 219-221, Mar. 1979. (Pubitemid 9443306)
19. H. V. Poor, "Fine quantization in signal detection and estimation," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 960-972, Sep. 1988.
20. G. R. Benitz and J. A. Bucklew, "Asymptotically optimal quantizers for detection of i.i.d. data," IEEE Trans. Inf. Theory, vol. 35, no. 2, pp. 316-325, Mar. 1989.
21. R. Gupta and A. O. Hero, III, "High-rate vector quantization for detection," IEEE Trans. Inf. Theory, vol. 49, no. 8, pp. 1951-1969, Aug. 2003.
22. J. Li, N. Chaddha, and R. M. Gray, "Asymptotic performance of vector quantizers with a perceptual distortion measure," IEEE Trans. Inf. Theory, vol. 45, no. 4, pp. 1082-1091, May 1999.
23. T. Linder, R. Zamir, and K. Zeger, "High-resolution source coding for nondifference distortion measures: Multidimensional companding," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 548-561, Mar. 1999.
24. J. A. Bucklew, "Multidimensional digitization of data followed by a mapping," IEEE Trans. Inf. Theory, vol. IT-30, no. 1, pp. 107-110, Jan. 1984.
25. A. Gersho and R. M. Gray, Vector Quantization and Signal Compression. Boston, MA: Kluwer Academic, 1992.
26. A. Gyorgy and T. Linder, "On the structure of optimal entropy-constrained scalar quantizers," IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 416-427, Feb. 2002. (Pubitemid 34491195)
27. T. Linder, "On asymptotically optimal companding quantization," Probl. Contr. Inf. Theory, vol. 20, no. 6, pp. 383-393, 1991.
28. R. M. Gray and D. L. Neuhoff, "Quantization," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2325-2383, Oct. 1998.
29. R. M. Gray and A. H. Gray Jr., "Asymptotically optimal quantizers," IEEE Trans. Inf. Theory, vol. 23, no. 1, pp. 143-144, Jan. 1977.
30. J. J. Y. Huang and P. M. Schultheiss, "Block quantization of correlated Gaussian random variables," IEEE Trans. Commun. Syst., vol. CS-11, no. 3, pp. 289-296, Sep. 1963.
31. B. Farber and K. Zeger, "Quantization of multiple sources using nonnegative integer bit allocation," IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 4945-4964, Nov. 2006. (Pubitemid 44680584)
32. I. Csiszar, "Generalized entropy and quantization problems," in Proc. Trans. 6th Prague Conf. Inf. Theory, Statist. Decis. Functions, Random Processes, 1973, pp. 29-35.
33. T. Linder and K. Zeger, "Asymptotic entropy-constrained performance of tessellating and universal randomized lattice quantization," IEEE Trans. Inf. Theory, vol. 40, no. 2, pp. 575-579, Mar. 1994.
34. M. Studený and J. Vejnarová, "The multiinformation function as a tool for measuring stochastic dependence," in Learning in Graphical Models, M. I. Jordan, Ed. Dodrecht: Kluwer Academic, 1998, pp. 261-297.
35. V. Misra, "Functional Quantization," M.Eng., Massachusetts Institute of Technology, Cambridge, MA, 2008.
36. A. György, T. Linder, and K. Zeger, "On the rate-distortion function of random vectors and stationary sources with mixed distributions," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 2110-2115, Sep. 1999. (Pubitemid 32077641)